**Time limit:**1.00 s**Memory limit:**512 MB

Each square of an 8 \times 8 chessboard has a robot. Each robot independently moves k steps, and there can be many robots on the same square.

On each turn, a robot moves one step left, right, up or down, but not outside the board. It randomly chooses a direction among those where it can move.

Your task is to calculate the expected number of *empty* squares after k turns.

# Input

The only input line has an integer k.

# Output

Print the expected number of empty squares rounded to six decimal places (rounding half to even).

# Constraints

- 1 \le k \le 100

# Example

Input:

10

Output:

23.120740